Dynamics in a discontinuous field: The smooth Fermi piston

G. A. Worrell, A. Matulich, B. N. Miller

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper we examine a version of the Fermi piston with a discontinuous, but nonimpulsive, periodic driving force. The dynamics of a particle moving in one spatial dimension are studied using a combination of numerical and analytical techniques. The configuration space of the particle is divided into two regions of constant acceleration that are of equal magnitude and opposite direction. The point of discontinuity F(t) dividing the regions changes periodically in time. The method of surface-of-section is used to study the phase space (φn, υn), where φn is the phase of the driving function and υn is the velocity of the particle at the nth encounter between the particle and boundary. We show that it is not possible to stochastically drive up the energy indefinitely except for the cases where F is discontinuous, or dF/dt is not finite everywhere. In addition, we find a new mechanism, other than KAM tori, for segmenting the phase space. As in the KAM picture, the central cause of the new behavior is resonance between the natural period of the particle and the period of the driving force. The boundaries to diffusion for continuous driving functions result from parabolic fixed points that span the entire phase range.

Original languageEnglish (US)
Pages (from-to)397-404
Number of pages8
Issue number3
StatePublished - 1993

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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